In the framework of MC methods, the idea of SC – based on the probability integral transformGiven the two random variables \(X,Y\) , with CDFs \(F_X,F_Y\) , it holds: \(F_X(X)\overset{{\rm d}}{=}F_Y(Y)\) . – is to approximate the relationship between a “computationally expensive” random variable, say \(A\) , and a “computationally cheap” one, say \(\xi \) . The approximation is then used for sampling. A random variable is “expensive” if its inverse CDF is not known in analytic form, and needs to be computed numerically. With SC, the sampling of \(A\)  is performed at the cost of sampling \(\xi \)  (see [1]}). Formally, the following mapping is used to generate samples from \(A\) :
\(A \overset{{\rm d}}{=} F_A^{-1}(F_{\xi }(\xi ))=: g(\xi )\approx \tilde{g}(\xi ),\) 
